I'm a bit skeptical on backgammon too after playing the 'real' (non-capturing) version against turks/lebanese. Certainly it's not chess, but substantially complex.
It's even provoked at least one advance in game theory. Some mathematicians at (iirc) the University of Alberta tried to use game theory to analyze poker, and found it was intractable. That led them to invent a systematic way to approximate complex games. (They built some good poker bots out of it, too, and sold one version as a training tool.)
Go has also provoked some interesting developments in Combinatorial Game Theory. Conway got started with "On Numbers and Games" (http://en.wikipedia.org/wiki/On_Numbers_and_Games) basically got started by analysing end-game situation in Go.
Note: Combinatorial Game Theory has almost no overlap with Game Theory. Interestingly Combinatorial Game Theory has some analogies in topology. You can for example give meaning to the temperature of a game.
uhhh, if it's "much deeper than chess" then it definitely takes decades to master.
One shouldn't claim to be deeper than chess without knowing the first thing about how much it's possible to study chess.